I. Field of the Invention
The present invention relates generally to generating multiple-access codes, and particularly to providing an asymptotically optimal decoding algorithm for generating multiple-access codes.
II. Description of the Related Art
Code Division Multiple Access (CDMA) systems, such as direct-sequence CDMA (DS-CDMA), multi-carrier CDMA, multi-code CDMA, spread-OFDM, and other types of CDMA systems, commonly suffer from multiple-access interference (MAI). When a user is assigned multiple orthogonalizing codes, signal degradation can take the form of inter-symbol interference (ISI). MAI (and ISI) is typically reduced by selecting orthogonalizing codes having low cross-correlations. However, in order to achieve good spreading characteristics in a DS-CDMA system, it is necessary to employ sequences having a low average mean-square aperiodic autocorrelation considering non-zero lags.
In practice, decoding errors are minimized by using distinctive multiple-access codes with suitable autocorrelation and cross-correlation properties. The cross-correlation between any two codes should be low for minimal interference between multiple users in a communications system or between multiple target reflections in radar and positioning applications. At the same time, it is desirable for the autocorrelation property of a multiple-access code to be steeply peaked, with small side-lobes. Maximally peaked code autocorrelation yields optimal acquisition and synchronization properties for communications, radar and positioning applications. Unfortunately, favorable autocorrelation characteristics are typically achieved at the expense of cross-correlation characteristics, and vice versa.
Code selection typically involves a trade-off between autocorrelation and cross-correlation performance. Various code-design techniques are described in D. V. Sarwate, “Mean-square correlation of shift-register sequences,” Proc. IEEE, vol. 131(2), April 1984, pp. 795-799, K. Yang, et. al., “Quasi-orthogonal sequences for code-division multiple-access systems,” IEEE Trans. Inform. Theory, vol. 46, pp. 982-992, May 2003, in P. V. Kumar and O. Moreno, “Prime-phase sequences with periodic correlation properties better than binary sequences,” IEEE Trans. Inform. Theory, vol. 37, pp. 603-616, May 1991, and in I. Oppermann and B. S. Vucetic, “Complex spreading sequences with a wide range of correlation properties,” IEEE Trans. Commun., vol. 45, pp. 365-375, November 1997, which are hereby incorporated by reference.
Various code-selection techniques have been developed, including artificial-intelligence approaches to complex signature sequence estimation, such as described in E. Buehler, B. Natarajan, and S. Das, “Multiobjective genetic algorithm based complex spreading code sets with a wide range of correlation properties,” in Proc. 15th International Conference on Wireless Communications, Vol. 2, Calgary, Alberta, Canada, 2003, pp. 548-552, and in B. Natarajan, S. Das, and D. Stevens, “Design of Optimal Complex Spreading Codes for DS-CDMA Using an Evolutionary Approach,” in Proc. Global Communications Conference, Dallas, November 2004, which are hereby incorporated by reference.